Final answer:
To determine the concentration of Cu2+ in a galvanic cell reaction involving Cu and Au3+, the Nernst equation is used, incorporating the given cell potential, standard cell potential, and the concentration of Au3+. The number of electrons transferred in the reaction is 6. The concentration of Cu2+ is calculated through the antilog of the rearranged Nernst equation.
Step-by-step explanation:
To calculate the concentration of Cu2+ in the given galvanic cell reaction (3Cu + 2Au3+ → 3Cu2+ + 2Au), the Nernst equation is used. The equation relates the cell potential (Ecell) to the standard cell potential (E°cell) and the reaction quotient (Q).
Using the Nernst equation:
Ecell = E°cell - (0.0592/n) × log(Q)
Given values are:
- Ecell = 1.15 V
- E°cell = 1.16 V
- [Au3+] = 0.4 M
The number of electrons transferred in the reaction (n) is 6, as there are 3 moles of Cu oxidized (each losing 2 electrons) and 2 moles of Au3+ reduced (each gaining 3 electrons).
By rearranging the Nernst equation and solving for the concentration of Cu2+, we get:
- = -(0.0592/6) × log(Q)
1.15V - 1.16V = -(0.0592/6) × log([Cu2+]3/0.42)
Rearranging gives the concentration of Cu2+ required to satisfy the above equation. By using the antilogarithm, we can find out the exact concentration of Cu2+.